A computer system typically employs a memory "backup" arrangement for storing copies of system files and programs. In such systems the backup memory may be either magnetic tape or a disk memory. An operator periodically replaces the backup memory with a new tape or disk, and stores the backup in a library of such tapes or disks. To access a particular file stored in the backup memory, then, the operator first has to locate in the library the magnetic tape or disk memory containing the file, and then load the contents of the tape or disk into the backup system. It can be appreciated that such an arrangement is labor intensive. A more efficient arrangement uses large scale memory, such as optical disks, which can store a very large number of backup files, thereby eliminating the need to maintain a library of magnetic tapes or disks. In the latter arrangement, each time a file is stored in the backup memory its storage location in the backup memory as well as its name and version number are stored in a Table of file names. Thus, the location of a file stored in the backup memory can be quickly ascertained by referring to the Table of file names. I have recognized, however, that 10%-15% of the capacity of the backup memory needs to be reserved to maintain such a Table. The reason for this is that, after a period of time, an appreciable number of entries (records) in the Table would contain the same file name, but different version numbers. Thus, in the case where a large number of files of different names are stored in the backup and each of those file names is associated with a number of different versions, then the entries in the Table would indeed consume an appreciable amount of the storage capacity of the backup memory.